02-03ChapGere.0003 - 108 A-PDF Axially Loaded Purchase...

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108 CHAPTER 2 Axially Loaded Members Solution 2.5-5 Bar with nonuniform temperature change At distance x : R EMOVE THE SUPPORT AT END B OF THE BAR : Consider an element dx at a distance x from end A . ¢ T ¢ T B ¢ x 3 L 3 d Elongation of element dx elongation of bar C OMPRESSIVE FORCE P REQUIRED TO SHORTEN THE BAR BY THE AMOUNT C OMPRESSIVE STRESS IN THE BAR s c P A E ( ¢ T B ) 4 P EA L 1 4 EA ( ¢ T B ) L 0 d L 0 ( ¢ T B ) ¢ x 3 L 3 dx 1 4 ( ¢ T B ) L d ( ¢ T ) dx ( ¢ T B ) ¢ x 3 L 3 dx L A T T B B x 0 L A B x dx Problem 2.5-6 A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion is 100 10 6 /°C. The
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